Light dots Animation Nodes
First, instance a sphere a certain number of times and position them based on a number of random vectors.



Then, we create a material for those objects such that its emission color is initially zero and randomly increases to become one. The random output of the Object Info node ranges between zero and one, if we subtract one from it and clamp the result, it will be zero, if we add one to it and clamp the result, it will be one. So if we add to it a value that animates from negative one to one and clamp the result, we get the result we are looking for. The animating can be done through the Cycles material Output and Animate Float nodes.



Then, we will use the Find Close Points node to create connections between the dots.



Finally, by animating the Bevel End of the splines, we can make them grow as follows.